Statistical linearization-based optimal tuning of tuned mass nonlinear damper inerter for seismic response mitigation of buildings with hysteretic inter-story isolation

Inter-storey isolation is a passive seismic protection strategy that uses flexible bearings to create an intermediate isolated story (IS) in multi-story buildings.The system makes a versatile seismic protection strategy, particularly attractive in redevelopment and/or seismic retrofitting of dual-purpose buildings.However, several challenges arise in IS-equipped buildings, including excessive drifts of the IS.Previous studies explored the coupling of IS with linear supplemental devices like fluid viscous dampers (FVDs) and inerter-based vibration absorbers.This paper extends these efforts by optimally designing a hybrid IS system with nonlinear isolators a tuned mass nonlinear damper inerter (IS-TMDI).In the IS-TMDI system, a nonlinear FVD following a power damping force-velocity law is the primary seismic energy dissipation device.Further, the nonlinear behaviour of the isolators is captured using the Bouc-Wen model.Hence, the paper puts forth a statistical linearization (SL) approach for the optimal IS-TMDI tuning and assessment to efficiently accommodate the nonlinear terms.In this approach, the seismic excitation is modelled as a stationary filtered Kanai-Tajimi stochastic process, assuming soft soil conditions.The numerical work considers a benchmark 20-story shear frame building, with the IS-TMDI positioned at four different intermediate floors.An additional configuration with a TMDI placed at an isolated rooftop (IR-TMDI), previously introduced by the authors for seismic retrofitting of existing buildings, is further included in the comparative study.Stationary displacement response variance data obtained from SL reveal that the low-floor IS-TMDI placements are more efficient in suppressing seismic building storey drift demands, while contrary to IR-TMDI, the IS-TMDI performance is insensitive/robust to the adopted optimal tuning criterion.Further, the practically important IS displacement demands are effectively regulated by the inertance ratio of the TMDI.Thus, the reported data demonstrate good potential of the IS-TMDI for seismic protection of buildings, paving the way for further fruitful research for a variety of buildings under recorded ground motions.